THE NORMALIZED LAPLACIAN ESTRADA INDEX OF GRAPHS

چکیده مقاله

Suppose G is a simple graph. The ℓ−eigenvalues δ1, δ2, . . . , δn of G are the eigenvalues of its normalized Laplacian ℓ. The normalized Laplacian Estrada index of the graph G is defined as ℓEE = ℓEE(G) = Σ n i=1 e δi . In this paper the basic properties of ℓEE are investigated. Moreover, some lower and upper bounds for the normalized Laplacian Estrada index in terms of the number of vertices, edges and the Randic index are obtained. In addition, some relations between ℓEE and graph energy Eℓ(G) are presented.